Mensuration

11. The average of the areas of 2 similar triangles is 706.5 m² whose perimeters are in the ratio of 6:11. What is 20% of the difference (in m²) in areas of both triangles ? [SSC CHSL 08/07/2024 (1st Shift)]

(a) 164
(b) 149
(c) 153
(d) 157

Correct Answer: (c) 153

Solution:

12. Two equal circles are drawn on a square in such a way that opposite side of the square forms the diameter of each circle. If the remaining area of the square is 42 cm², what is the measurement (in cm) of the diameter of each circle? [SSC CHSL 02/07/2024 (2nd Shift)]

(a) 14
(b) 2.5
(c) 7
(d) 3.5

Correct Answer: (a) 14

Solution:

13. The ratio of the diameters of two spheres is given as 1:4. The larger sphere is melted and 125 identical spheres are made out of the molten material. The smaller sphere is melted and 27 identical spheres are made out of the molten material. If the ratio of the volume of each of the 125 identical spheres to the volume of each of the 27 identical spheres is given as 1: m, what is the value of m? [SSC CHSL 01/07/2024 (1st Shift)]

(a) 1728/125
(b) 125/1728
(c) 27/8000
(d) 64/3375

Correct Answer: (b) 125/1728

Solution:

14. Two rectangular sheets of paper, each 60 cm x 36 cm, are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is: [SSC CPO 29/06/2024 (3rd Shift)]

(a) 5:6
(b) 8:3
(c) 7:4
(d) 5:3

Correct Answer: (d) 5:3

Solution:

15. Three circles each of radius 5 cm touch one another. The area (in cm²) subtended between them is: [SSC CPO 28/06/2024 (3rd Shift)]

Correct Answer: (d)

Solution:

16. A gear 15 cm in diameter is turning a gear 21 cm in diameter. When the smaller gear has 105 revolutions, how many has the larger one made ? [SSC CPO 28/06/2024 (3rd Shift)]

(a) 75
(b) 100
(c) 85
(d) 90

Correct Answer: (a) 75

Solution:

17. A solid metal cylinder of 12 cm height and 7 cm radius is melted and recast into two cones in the proportion of 1:2 (volume), keeping the height 12 cm. What would be the percentage change in the flat surface area before and after [use π = 22/7] [SSC CPO 28/06/2024 (3rd Shift)]

(a) 35%
(b) 20%
(c) 45%
(d) 50%

Correct Answer: (d) 50%

Solution:

18. Three solid iron cubes of edges 8 cm, 10 cm and 12 cm are melted together to make a new cube. It is observed that 496 cm³ of the melted material is lost due to improper handling. The area (in cm²) of the whole surface of the newly formed cube is: [Matriculation Level 26/06/2024 (Shift -1)]

(a) 1331
(b) 1176
(c) 2197
(d) 3375

Correct Answer: (b) 1176

Solution:

19. If the semi-perimeter and area of a rectangular field whose length and breadth are 'x' and 'y' is 12 cm and 28 cm², respectively, then find the value of x⁴ + x²y² + y⁴. [Graduate Level 20/06/2024 (Shift-3)]

(a) 6690
(b) 6960
(c) 6609
(d) 6906

Correct Answer: (b) 6960

Solution:

20. The base of a right prism is an equilateral triangle with each side measuring 4 cm. If the lateral surface area is 120 cm², find the volume (in cm³) of the prism. [SSC CHSL Tier II (10/01/2024)]

(a) 30√3
(b) 40√3
(c) 10√3
(d) 20√3

Correct Answer: (b) 40√3

Solution:

Mensuration

11. The average of the areas of 2 similar triangles is 706.5 m² whose perimeters are in the ratio of 6:11. What is 20% of the difference (in m²) in areas of both triangles ? [SSC CHSL 08/07/2024 (1st Shift)]

12. Two equal circles are drawn on a square in such a way that opposite side of the square forms the diameter of each circle. If the remaining area of the square is 42 cm², what is the measurement (in cm) of the diameter of each circle? [SSC CHSL 02/07/2024 (2nd Shift)]

14. Two rectangular sheets of paper, each 60 cm x 36 cm, are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is: [SSC CPO 29/06/2024 (3rd Shift)]

15. Three circles each of radius 5 cm touch one another. The area (in cm²) subtended between them is: [SSC CPO 28/06/2024 (3rd Shift)]

16. A gear 15 cm in diameter is turning a gear 21 cm in diameter. When the smaller gear has 105 revolutions, how many has the larger one made ? [SSC CPO 28/06/2024 (3rd Shift)]

17. A solid metal cylinder of 12 cm height and 7 cm radius is melted and recast into two cones in the proportion of 1:2 (volume), keeping the height 12 cm. What would be the percentage change in the flat surface area before and after [use π = 22/7] [SSC CPO 28/06/2024 (3rd Shift)]

18. Three solid iron cubes of edges 8 cm, 10 cm and 12 cm are melted together to make a new cube. It is observed that 496 cm³ of the melted material is lost due to improper handling. The area (in cm²) of the whole surface of the newly formed cube is: [Matriculation Level 26/06/2024 (Shift -1)]

19. If the semi-perimeter and area of a rectangular field whose length and breadth are 'x' and 'y' is 12 cm and 28 cm², respectively, then find the value of x⁴ + x²y² + y⁴. [Graduate Level 20/06/2024 (Shift-3)]

20. The base of a right prism is an equilateral triangle with each side measuring 4 cm. If the lateral surface area is 120 cm², find the volume (in cm³) of the prism. [SSC CHSL Tier II (10/01/2024)]

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